3D Bayesian image reconstruction using the generalized EM algorithm

Abstract

Summary form only given. The use of the generalized expectation maximization (GEM) algorithm for image reconstruction from projections and restoration from broad point spread functions is proposed. A GEM algorithm has been developed for maximum a posteriori (MAP) estimation using Markov random field prior distributions for a set of Poisson data whose mean is related to the unknown image by a linear transformation. This method is applicable in emission tomography (PET and SPECT) and to the restoration of radioastronomical images. The EM algorithm is applicable to problems in which there is a more natural formulation of the estimation problem in terms of a set of complete unobserved data which is related to the incomplete observed data by a known many-to-one transformation. Applying this approach to the MAP image reconstruction problem results in a two-step iterative algorithm. The resulting computational costs are significantly lower than those for the coordinate descent algorithms. The algorithm does not guarantee convergence to a global maximum, but will converge to a stationary point of the posterior density for the image conditional on the observed data.<>